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"fundamentally determine" is a correct and usable phrase in written English.
It means to have a significant influence or impact on something. You can use it to describe the root cause or underlying factors that determine the outcome of a situation. Example: The quality of education received in early childhood can fundamentally determine a person's success in life.
Exact(6)
"How we build our cities and our transport, and how we build our energy systems over the next 20 or so will fundamentally determine our chances of holding to within 2C," he said.
Since soil properties fundamentally determine how vegetation will grow, substrate effects shall be discussed first.
However, the tracking module derives the vehicle trajectories, whose accuracy will fundamentally determine the accuracy of collected traffic data.
Before you yawn and click away, bear in mind: these wonky decisions will fundamentally determine the future of everything you read, watch, and listen to, maybe for generations.
In fact, my wardrobe selection for the day would fundamentally determine how sane I was going to be, and if I wasn't able to find a loose shirt or something to mask the outline of my nipples, I would skip appointments, class, work.
The limits of the r2 and p values in the statistical meaningfulness definition fundamentally determine (table 2) which time series should be considered statistical meaningful.
Similar(54)
As Rosa deftly shows, this self-reinforcing feedback loop fundamentally determines the character of modern life.
Where people live, work, shop, and recreate fundamentally determines their local travel options.
At high beam current, the resolution of the ptychography reconstruction is fundamentally determined by the collection angle of the detector.
Properties of metals are fundamentally determined by their electron behavior, which is largely reflected by the electron work function.
I don't doubt these critics' sincerity; I think that their responses were not fundamentally determined by these reports, only intensified by them.
More suggestions(15)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com